Continuous procedure of stochastic approximation in a semi-Markov medium
Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation $$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$ in a random semi-Markov medium described by an ergodic semi-Markov process $x(t)$.
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| Datum: | 2004 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3792 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509925753487360 |
|---|---|
| author | Chabanyuk, Ya. M. Чабанюк, Я. М. |
| author_facet | Chabanyuk, Ya. M. Чабанюк, Я. М. |
| author_sort | Chabanyuk, Ya. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:08:43Z |
| description | Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation
$$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$
in a random semi-Markov medium described by an ergodic semi-Markov process $x(t)$. |
| first_indexed | 2026-03-24T02:48:51Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3792 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T02:48:51Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/39/f1d2c739fefd864aad9dc48c8ecdee39.pdf |
| spelling | umjimathkievua-article-37922020-03-18T20:08:43Z Continuous procedure of stochastic approximation in a semi-Markov medium Неперервна процедура стохастичпої апроксимації у напівмарковському середовищі Chabanyuk, Ya. M. Чабанюк, Я. М. Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation $$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$ in a random semi-Markov medium described by an ergodic semi-Markov process $x(t)$. Встановлено умови збіжності процедури стохастичпої апроксимації $$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$ у випадковому напівмарковському середовищі, що описується ергодичним напівмарковським процесом $x(t)$, з використанням функції Ляпунова для усередненої системи. Institute of Mathematics, NAS of Ukraine 2004-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3792 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 5 (2004); 713–720 Український математичний журнал; Том 56 № 5 (2004); 713–720 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/3792/4305 https://umj.imath.kiev.ua/index.php/umj/article/view/3792/4306 Copyright (c) 2004 Chabanyuk Ya. M. |
| spellingShingle | Chabanyuk, Ya. M. Чабанюк, Я. М. Continuous procedure of stochastic approximation in a semi-Markov medium |
| title |
Continuous procedure of stochastic approximation in a semi-Markov medium |
| title_alt | Неперервна процедура стохастичпої апроксимації у напівмарковському середовищі |
| title_full |
Continuous procedure of stochastic approximation in a semi-Markov medium |
| title_fullStr |
Continuous procedure of stochastic approximation in a semi-Markov medium |
| title_full_unstemmed |
Continuous procedure of stochastic approximation in a semi-Markov medium |
| title_short |
Continuous procedure of stochastic approximation in a semi-Markov medium |
| title_sort | continuous procedure of stochastic approximation in a semi-markov medium |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3792 |
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